Transcendence and linear relations of 1-periods

This exploration of the relation between periods and transcendental numbers brings Baker's theory of linear forms in logarithms into its most general framework, the theory of 1-motives.

Written by leading experts in the field, it contains original results and finalises the theory of linear relations of 1-periods, answering long-standing questions in transcendence theory.

It provides a complete exposition of the new theory for researchers, but also serves as an introduction to transcendence for graduate students and newcomers.

It begins with foundational material, including a review of the theory of commutative algebraic groups and the analytic subgroup theorem as well as the basics of singular homology and de Rham cohomology.

Part II addresses periods of 1-motives, linking back to classical examples like the transcendence of , before the authors turn to periods of algebraic varieties in Part III.

Finally, Part IV aims at a dimension formula for the space of periods of a 1-motive in terms of its data.